ODE
\[ 2 y(x) y''(x)=f(x) y(x)^2+3 y'(x)^2 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 10.7537 (sec), leaf count = 0 , could not solve
DSolve[2*y[x]*Derivative[2][y][x] == f[x]*y[x]^2 + 3*Derivative[1][y][x]^2, y[x], x]
Maple ✓
cpu = 0.202 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{2}}+{\frac {f \left ( {\it \_a} \right ) }{2}} \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[2*y[x]*y''[x] == f[x]*y[x]^2 + 3*y'[x]^2,y[x],x]
Mathematica raw output
DSolve[2*y[x]*Derivative[2][y][x] == f[x]*y[x]^2 + 3*Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = 3*diff(y(x),x)^2+f(x)*y(x)^2, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(exp(Int(_b(_a),_a)+_C1),[{diff(_b(_a),_a) = 1/2*_b(_a)^2+1/2*f(_a)}, {_a = x, _b(_a) = diff(y(x),x)/y(x)}, {x = _a, y(x) = exp(Int(_b(_a),_a)+_C1)}])